Open Access
Add to BibSonomy
Abstract
We successfully fabricate a transversely disordered optical fiber made of AsSe2 and As2S5 glasses for high-resolution mid-infrared image transport. By using the fabricated fiber, we experimentally observe transverse Anderson localization of mid-infrared light at the wavelength of 3 µm. Moreover, we numerically evaluate the localization in the fiber by using a cross-sectional image of the fiber.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Anderson localization was found as the absence of electron-waves in disordered media [1] and then observed in various other wave phenomena [2–5]. Transverse Anderson localization (TAL) of light was proposed by H. de Raedt et al. [6,7]. After the theoretical proposal, TAL of light was experimentally demonstrated in several two-dimensional optical media. TAL of light requires the refractive index distribution that is random in the transverse direction but invariant in the longitudinal direction. TAL of visible light was observed in a disordered two-dimensional photonic lattice [8], and then in a transversely disordered optical fiber (TDOF) [9,10]. By using TDOFs, optical image transport was demonstrated in the visible [11,12] and near-infrared region [13,14].
Mid-infrared (MIR) imaging has great potential for biomedical applications. Many fundamental molecular vibration absorptions are included in the MIR region [15,16]. Moreover, the peak wavelength of thermal emission at human body temperature is about 9.3 µm in the MIR region. Thus, MIR images provide the temperature with non-contact and non-invasive [17]. Chalcogenide glasses are used as materials of MIR optical fibers, some of which can transport MIR optical image [18–20]. However, no results have ever been reported on TAL and optical image transport of the MIR light in TDOFs.
In this paper, we have successfully fabricated a transversely disordered optical fiber made of chalcogenide glasses, chalcogenide TDOF (Ch-TDOF). We have observed the TAL of MIR light in the Ch-TDOF for the first time, to our best knowledge. We numerically investigated the localization by using a cross-sectional image of the fabricated Ch-TDOF in order to optimize fiber parameters for high-resolution MIR image transport.
2. Materials and fabrication process
2.1 Material properties
Material transparency is important for light propagation with low attenuation. We selected AsSe${_2}$ and As$_{2}$S$_{5}$ from chalcogenide glasses as materials of a Ch-TDOF because of their small difference in thermal properties and their high thermal stabilities. This pair was also used in [21,22] for the propagation of the MIR light. Figure 1 shows the transmittance of AsSe${_2}$ and As$_{2}$S$_{5}$ glasses in the wavelength range of 2–20 µm measured by using an FT-IR spectrometer (Perkin Elemer, Spectrum 100). The transmission range of AsSe${_2}$ can reach 20 µm.
Fig. 1. Transmission spectra of AsSe${_2}$ and As$_{2}$S$_{5}$ glasses. The thickness of the samples was 1 mm.
The refractive indices of materials of TDOFs are also important for strong localization, that is, large difference of refractive indices enables a small beam diameter. The refractive indices were obtained at the wavelengths from 2 µm to 4.5 µm by the minimum deviation method with a precision spectrometer (Shimadzu, GMR-1), and at the wavelengths from 4.5 µm to 12 µm by the Swanepoel method [23]. The Swanepoel method determines the refractive index from interference fringes of a transmission spectrum with a thin sample. This method also was used in order to obtain the refractive index dispersion of chalcogenide glasses in [24]. The transmission spectra of AsSe${_2}$ and As$_{2}$S$_{5}$ thin samples were measured by using the FT-IR spectrometer. The thickness of AsSe${_2}$ and As$_{2}$S$_{5}$ glass samples was 190.5 and 169.5 µm. The measured refractive indices were fitted to the Sellmeier equation,
Table 1. Sellmeier coefficients of AsSe${_2}$ and As$_{2}$S$_{5}$ glasses.
2.2 Fabrication process
The fabrication of a Ch-TDOF required AsSe${_2}$ rods, As$_{2}$S$_{5}$ rods, and an As$_{2}$S$_{5}$ tube. Figure 3 shows a schematic diagram of the fabrication process of a Ch-TDOF. The fabrication process consists of three steps. Firstly, AsSe${_2}$ rods and As$_{2}$S$_{5}$ rods were drawn down into element fibers whose diameters were 125 µm. Figure 4(a) shows an image of element fibers made of these rods. Secondly, 2000 element fibers were randomly stacked together to obtain a bundle of fibers with transversely disordered index profile. The number of each element fiber (AsSe${_2}$ and As$_{2}$S$_{5}$ fibers) was 1000. Figure 4(b) shows an image of randomly stacked element fibers. This bundle of fibers was inserted into an As$_{2}$S$_{5}$ tube whose inner and outer diameters were 6 and 12 mm, respectively. Finally, they were drawn down to obtain a Ch-TDOF whose outer diameter was about 350 µm. During fiber drawing process, a negative pressure was applied to remove the interior air gap between each element fibers.
Fig. 4. Image of element fibers (a) made of AsSe2 and As2S5 glasses and (b) randomly mixed AsSe2 and As2S5 fibers.
3. Results and discussions
3.1 Fabrication results
Cross-sectional images of the fabricated Ch-TDOF were captured by using a scanning electron microscope (SEM) (JEOL, JSM-6490A) and shown in Fig. 5. In Fig 5, the bright regions are occupied by AsSe${_2}$ and dark regions are occupied by As$_{2}$S$_{5}$. No large gaps are observed in the cross section of the Ch-TDOF due to applying the negative pressure during the drawing process.
Fig. 5. SEM cross-sectional images of the fabricated Ch-TDOF. The diameter of the area of random refractive index distribution is 169 µm.
3.2 Observation of TAL of mid-infrared light
We demonstrated TAL of MIR by using a 6-cm-long Ch-TDOF, which was cleaved using a cleaver (Vytran, LDC401) to ensure both flat surfaces with no cracks. A light beam from a tunable femtosecond laser (Coherent, Chameleon) was coupled into the Ch-TDOF by using a lens (Thorlabs, C036TME-E). The wavelength of the beam was tuned to 3.0 µm. The output light collimated by a lens (Thorlabs, C028TME-E) was observed by using a MIR beam profiler (DataRay, WinCamD-IR-BB).
Figure 6 shows the near-field intensity profiles for 4 different launch positions. When an input position was moved, the localized light was shifted to the direction corresponding to the input movement. Figure 7 shows the intensity plots obtained from Fig. 6(d) along with vertical and horizontal direction. The smallest full width at half maximum (FWHM) of the localized light corresponding to vertical and horizontal direction is 14 and 11 µm as shown in Fig. 7. Figures 6 and 7 indicate that the incident light propagated as non-localized modes as well as localized modes. We must suppress the non-localized modes because these modes behave as background noise and reduce contrast of optical images.
Fig. 6. Near-field intensity profiles of the output light for different launch positions. These profiles are displayed under the same color bar scale. These profiles are collected under the same exposure time and displayed under the same color bar scale.
Fig. 7. Intensity plots of the localized beam profile of Fig. 6(d). The plots of (a) and (b) show the intensity on the horizontal and vertical lines through the maximum intensity point. Blue dashed lines are the fitted curves to the two-term Gaussian beam profiles.
4. Numerical simulation of localized modes of the Ch-TDOF with the different unit size of AsSe${_2}$ and As$_{2}$S$_{5}$ elements
We can optimize the unit size of AsSe${_2}$ and As$_{2}$S$_{5}$ elements of a Ch-TDOF in order to obtain smaller beam sizes. The smaller the beam size is, the higher the resolution of MIR image transport is. To estimate the expansion of the localized modes of the Ch-TDOF, we defined
where $S_{\rm {all}}$ is the area of random refractive index distribution, $S_{\rm {ele}}$ is the area of each element fiber, $N_{\rm {ele}}$ is the number of element fibers, $D_{\rm {all}}$ is the diameter of random refractive index distribution, and $D_{\rm {ele}}$ is the mean diameter of each element fiber. We obtain from Eqs. (2–3). In Fig. 5, $D_{\rm {ele}}$ is 3.8 µm, because $D_{\rm {all}}$ is 169 µm and $N_{\rm {ele}}$ is 2000. For estimating the difference of the localization between the difference of $D_{\rm {ele}}$, we definedFig. 8. Geometry of the Ch-TDOF for calculating localized modes. The refractive index is randomly distributed in the area enclosed by the red dashed line.
Figure 9 shows element diameter dependence of the average effective mode diameter of the 1st to 100th-order propagation modes for the wavelength of 3 µm ($\lambda =3\,\mathrm{\mu}\textrm{m}$). When $D_{\rm {ele}}/\lambda$ is 0.4, the average of effective mode diameter is the smallest. In our earlier paper regarding tellurite TDOFs [14], the refractive index difference is about 0.1. When $D_{\rm {ele}}/\lambda$ of the tellurite TDOFs is about 0.7, the area is the smallest. Moreover, B. Abaie et al. [25,26] discussed the element size dependence of the mode diameter.
Fig. 9. Element diameter dependence of the average effective mode diameter of the 1st to 100th-order propagation modes for the wavelength of 3 µm. The error bars are the statistical standard deviations of $D_{\rm {mode}}$. Red points were obtained from Fig. 7(a) and (b).
Although we can evaluate the diameter of each localized mode by numerical simulation, the intensity profiles of Fig. 7 include localized and non-localized modes. To separate the intensity profile of Fig. 7 from localized and non-localized modes and compare the numerical simulation and experimental results, we fitted the intensity profiles to the two-term Gaussian beam profiles of the form
Figure 10 shows element diameter dependence of the average effective mode diameter of the 1st to 100th-order propagation modes for the wavelengths of 3–11µm. At each wavelength, the average of effective mode diameter is the smallest with $D_{\rm {ele}}/\lambda$ = 0.4 because the refractive index difference is almost constant in this wavelength range.
Fig. 10. Element diameter dependence of the average effective mode diameter of the 1st to 100th-order propagation modes for the wavelengths of 3–11 µm. The error bars are the statistical standard deviations of $D_{\rm {mode}}$.
5. Conclusions
In this paper, we reported the fabrication of a transversely disordered optical fiber made of AsSe${_2}$ and As$_{2}$S$_{5}$ glasses. We showed the localization of the MIR light for different launch positions after the light propagated in a 6-cm-long Ch-TDOF. The results in longer Ch-TDOFs are expected to be achieved by further improving the fiber fabrication process. Moreover, we showed numerical simulation of localized modes of the fabricated Ch-TDOF in order to optimize the unit size of AsSe${_2}$ and As$_{2}$S$_{5}$. As a result, the small beam diameter can be obtained when the unit size is 0.4 times larger than the wavelength. Our future work will achieve high-resolution MIR image transport by using a Ch-TDOF whose unit size is optimized, and our next publication will report this work.
Funding
Japan Society for the Promotion of Science (19H02203).
Acknowledgement
We would like to thank his comments of this research theme by Professor K. Saito at Toyota Technological Institute.
Disclosures
The author declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958). [CrossRef]
2. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008). [CrossRef]
3. A. A. Chabanov, M. Stoytchew, and A. Z. Genack, “Statistical signatures of photon localization,” Nature 404(6780), 850–853 (2000). [CrossRef]
4. R. Dalichaouch, J. P. Armstrong, S. Schultz, P. Plantzman, and S. L. McCall, “Microwave localization by two-dimetial random scattering,” Nature 354(6348), 53–55 (1991). [CrossRef]
5. D. Laurent, O. Legrand, P. Sebbah, C. Vanneste, and F. Mortessagne, “Localized modes in a finite-size open disordered microwave cavity,” Phys. Rev. Lett. 99(25), 253902 (2007). [CrossRef]
6. H. de Raedt, A. Lagendijk, and P. de Vries, “Transverse Localization of Light,” Phys. Rev. Lett. 62(1), 47–50 (1989). [CrossRef]
7. S. S. Abdullaev and F. K. Abdullaev, “On propagation of light in fiber bundles with random parameters,” Radiofizika 23, 766–767 (2014).
8. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007). [CrossRef]
9. A. Mafi, S. Karbasi, K. W. Koch, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in disordered glass optical fibers: A review,” Opt. Mater. Express 2(11), 1496–1503 (2012). [CrossRef]
10. S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37(12), 2304–2306 (2012). [CrossRef]
11. S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5(1), 3362 (2014). [CrossRef]
12. J. Zhao, J. E. A. Lopez, Z. Zhu, D. Zheng, S. Pang, R. A. Correa, and A. Schülzgen, “Image transport through meter-Long randomly disordered silica-air optical fiber,” Sci. Rep. 8(1), 3065 (2018). [CrossRef]
13. T. H. Tuan, S. Kuroyanagi, T. Suzuki, and Y. Ohishi, “Infrared image transport through an all-solid tellurite optical glass rod with transversely-disordered refractive index profile,” Opt. Express 26(13), 16054–16062 (2018). [CrossRef]
14. T. H. Tuan, S. Kuroyanagi, K. Nagasaka, T. Suzuki, and Y. Ohishi, “Characterization of an all-solid disordered tellurite glass optical fiber and its NIR optical image transport,” Jpn. J. Appl. Phys. 58(3), 032005 (2019). [CrossRef]
15. C. R. Petersen, N. Prtljaga, M. Farries, J. Ward, B. Napier, G. R. Lloyd, J. Nallala, N. Stone, and O. Bang, “Mid-infrared multispectral tissue imaging using a chalcogenide fiber supercontinuum source,” Opt. Lett. 43(5), 999–1002 (2018). [CrossRef]
16. A. B. Seddon, “Mid-infrared (IR) - A hot topic: The potential for using mid-IR light for non-invasive early detection of skin cancer in vivo,” Phys. Status Solidi B 250(5), 1020–1027 (2013). [CrossRef]
17. B. B. Lahiri, S. Bagavathiappan, T. Jayakumar, and J. Philip, “Medical applications of infrared thermography: A review,” Infrared Physics & Technology 55(4), 221–235 (2012). [CrossRef]
18. M. Saito, M. Takizawa, S. Sakuragi, and F. Tanei, “Infrared image guide with bundled As–S glass fibers,” Appl. Opt. 24(15), 2304–2308 (1985). [CrossRef]
19. S. Qi, B. Zhang, C. Zhai, Y. Li, A. Yang, Y. Yu, D. Tang, Z. Yang, and B. Luther-Davies, “High-resolution chalcogenide fiber bundles for longwave infrared imaging,” Opt. Express 25, 4384–4387 (2018). [CrossRef]
20. A. Ventura, F. Ben Slimen, J. Lousteau, N. White, A. Masoudi, P. Janicek, and F. Poletti, “Flexible Mid-IR fiber bundle for thermal imaging of inaccessible areas,” Opt. Express 27(15), 20259–20272 (2019). [CrossRef]
21. T. Cheng, Y. Kanou, D. Deng, X. Xue, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Fabrication and characterization of a hybrid four-hole AsSe2-As2S5 microstructured optical fiber with a large refractive index difference,” Opt. Express 22(11), 13322–13329 (2014). [CrossRef]
22. T. Cheng, Y. Kanou, X. Xue, D. Deng, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Mid-infrared supercontinuum generation in a novel AsSe2-As2S5 hybrid microstructured optical fiber,” Opt. Express 22(19), 23019–23025 (2014). [CrossRef]
23. R. Swanepoel, “Determining refractive index and thickness of thin films from wavelength measurements only,” J. Opt. Soc. Am. A 2(8), 1339–1343 (1985). [CrossRef]
24. Y. Fang, D. Jayasuriya, D. Furniss, Z. Q. Tang, L. Sojka, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Determining the refractive index dispersion and thickness of hot-pressed chalcogenide thin films from an improved Swanepoel method,” Opt. Quantum Electron. 49(7), 237 (2017). [CrossRef]
25. B. Abaie and A. Mafi, “Scaling analysis of transverse Anderson localization in a disordered optical waveguide,” Phys. Rev. B 94(6), 064201 (2016). [CrossRef]
26. B. Abaie and A. Mafi, “Modal area statistics for transverse Anderson localization in disordered optical fibers,” Opt. Lett. 43(16), 3834–3837 (2018). [CrossRef]
